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Lipschitz changes of variables via heat flow

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arxiv 2201.03403 v1 pith:MHLYGPP5 submitted 2022-01-10 math.PR

Joe Neeman This is my paper · ORCID
classification math.PR
keywords changesvariablesflowheatlipschitzapproachargumentcaffarelli
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We extend Caffarelli's contraction theorem, by proving that there exists a Lipschitz changes of variables between the Gaussian measure and certain perturbations of it. Our approach is based on an argument due to Kim and Milman, in which the changes of variables are constructed using a heat flow.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal transport maps, majorization, and log-subharmonic measures

    math.AP 2024-11 conditional novelty 7.0 of 10

    A trace-level analogue of Caffarelli's contraction theorem is proved for log-subharmonic sources, yielding majorization, entropy stability, and new proofs of Wehrl-type inequalities.

  2. Smooth transport map via diffusion process

    math.PR 2024-11 conditional novelty 7.0 of 10

    The heat-flow transport map (Föllmer/Langevin) pushing the Gaussian onto a log-Hölder perturbation of the Gaussian is shown to be C^{β+1}-smooth, with applications to functional inequalities, GAN estimation, and diffu...

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